Here's a "fact sheet" from Save-Our-Kids.com contradicting so called "myths" about child molesters and offering contradicting statements. I did not see a link to the data they used to create this page so take it with a grain of salt:

Child Molester - Myths & Realities

Myth 1: The child molester is a dirty old man.
Truth - Over 70% of offenders are under the age of 35:
74% have one or more prior convictions
and of these 80% were under 30 years of age.

Myth 2: The child molester is a stranger.
Truth - Over 70% of the molesters knew the children at least casually;
14% are members of the child’s immediate family.

Myth 3: The child molester is retarded.
Truth - No differences between convicted child molesters
intellectual abilities and that of the general public.

Myth 4: The child molester is an alcoholic or drug addict.
Truth - Drug use is usually non-existent with child molesters
except to break down child inhibitions.

Myth 5: The child molester is a sexually frustrated person.
Truth - 50% of child molesters are married.
Sexuality is not the only issue in pedophilia but identification
expression problems and the need for power and control
which usually is existent with adult relationships.

Myth 6: The child molester is insane.
Truth - 95% are not psychotic.

Myth 7: The child molester over time will progress to increasingly violent acts.
Truth - Only about 18% of child molesters show an increase in force used.
9% committed violent sexual assaults- 1% resulting in death.

Myth 8: Children are at greater risk of sexual victimization from homosexuals
than from heterosexuals adults.
Truth - 51% of men selected female children.
21% selected both. Females victimized 2-1.
83% of child molesters are heterosexual.

Myth 12: Child molesters commit other crimes.
Truth - Approximately 50% of convicted child molesters have no other criminal record.

Child molester (Basic Profile)

Relatively young heterosexual man - not insane - no retardation.
Seeks to control child rather than injure.
Poses more psychological risk than physical risk to the child.
Highly repetitive behavior to the point of compulsion.